Question

transformations test (topic 4)
if a figure is translated with the rule ( t_{langle -5, 3
angle} ), which translation moves the image back to the original position?
( \bigcirc t_{langle 5, 3
angle} )
( \bigcirc t_{langle -5, 3
angle} )
( \bigcirc t_{langle 5, -3
angle} )
( \bigcirc t_{langle -5, 0
angle} )

Explanation:

Step1: Understand Translation Rule

A translation \( T_{\langle a,b
angle} \) moves a point \((x,y)\) to \((x + a,y + b)\). To reverse a translation \( T_{\langle - 5,3
angle} \) (which moves \((x,y)\) to \((x-5,y + 3)\)), we need a translation that undoes these changes. Let the reverse translation be \( T_{\langle c,d
angle} \), so \((x-5 + c,y + 3 + d)=(x,y)\). This implies \( - 5 + c=0\) and \(3 + d = 0\). Solving for \(c\) and \(d\), we get \(c = 5\) and \(d=-3\). So the reverse translation is \( T_{\langle 5,-3
angle} \).

Step2: Match with Options

Looking at the options, the translation \( T_{\langle 5,-3
angle} \) (assuming the third option is \( T_{\langle 5,-3
angle} \) as per the notation) is the one that reverses \( T_{\langle - 5,3
angle} \).

Answer:

\( T_{\langle 5,-3
angle} \) (the third option among the given choices)